Multilevel inverter control schemes

ABSTRACT

A multilevel inverter control system having logic configured to substantially minimize an area difference between a target waveform and a step signal of a multilevel inverter.

BACKGROUND OF THE INVENTION

[0001] 1. Field of the Invention

[0002] The present invention relates generally to the field of directcurrent-to-alternating current (DC/AC) inverters, and more particularlyto control schemes for a multilevel inverter.

[0003] 2. Description of the Related Art

[0004] A DC/AC inverter changes DC power into AC power. In a PWM (pulsewidth modulation) controlled inverter, DC voltage is “chopped” intopulses. The mean value of the pulses follows a sinusoidal waveform.Depending on the power rating of the inverter, the switching frequencycan range from a few kHz to a few tens of kHz. There are two main issuesamongst many others in design of such an inverter-high switching powerloss and high electric magnetic interference (EMI).

[0005] One of the alternatives to PWM controlled inverter schemes is touse a multilevel voltage source inverter. A multilevel inverter is apractical approach when an output transformer is required at the loadside for safety reasons. Standard products with power ratings of around5 kW are available in the market, such as the SW series from TraceEngineering, 5916 195th St. N.E. Arlington, Wash. USA 98223. Theadvantages of using a multilevel inverter over a PWM controlled inverterinclude very good surge capability, high efficiency, good voltage andfrequency regulation, and low total harmonic distortion (THD).

[0006]FIG. 1 shows a typical configuration of a multilevel inverter 100.A single DC power source 102 provides power to several low-frequencyH-bridge circuits 104 and output transformers 106. The number oflow-frequency H-bridge circuits 104 and output transformers 106 is oftendetermined by specific application requirements.

[0007] Each H-bridge circuit 104 may generate a zero voltage or apositive/negative step voltage at its output. A series connection 108 ofthe output transformers 106 provides a multilevel voltage waveform to anAC load (not shown).

[0008]FIG. 2 shows an output voltage waveform of the multilevel inverter100, which can be used to generate an approximation of a desired outputvoltage waveform (see FIG. 4). The voltage “steps” shown in FIG. 2 areassociated with energizing the individual output transformers 106 inseries connection 108 (FIG. 1) in various and different ways, asexplained below. With respect to each individual output transformer 106,the transformer output voltage is proportional to the number of turns ofthe transformer windings. For a specific application, the number ofturns of a winding is fixed.

[0009] There are many possible transformer turn ratio configurations.For example, assume the turn ratio between the three transformer outputwindings (W1, W2, W3) is 9:3:1. The corresponding voltage ratio willalso be 9:3:1. With this voltage ratio, assuming the waveform is quartersymmetrical, a possible composition for a quarter cycle may be designedas, Step No. 1 2 3 4 5 6 7 8 9 10 11 12 13 Output 1 (3 − 1) 3 (3 + 1) (9− 3 − 1) (9 − 3) (9 − 3 + 1) (9 − 1) 9 (9 + 1) (9 + 3 − 1) (9 + 3) (9 +3 + 1)

[0010] At step 1, W3 is energized to positive step voltage, while W1 andW2 are not energized. At step 2, W2 is energized to positive, W3 isenergized to negative, while W1 is not energized. Similarly, 13 voltagesteps are created in the first half cycle with equalized voltageincrease at each step. A maximum of 27 (including zero) voltage stepsmay be created within each cycle (60 Hz). The number of steps per cyclerequired is based on the level of DC input voltage and the percentage ofoutput load.

[0011] Once the voltage steps are fixed, the times at which the stepvoltages occur (also referred as switching times) are specified. Thereare many related art approaches to calculating the switching time.Harmonics elimination and harmonics minimization schemes are two of theoptimal approaches.

[0012] Detailed optimal calculation of switching time based on themathematical theory of harmonics elimination and harmonics minimizationschemes is complicated and time consuming. See J. Chiasson, etc.,“Real-Time Computer Control of a Multilevel Converter using theMathematical Theory of Resultants”, Electrimacs, August 2002.Consequently, practical real time applications of such related artschemes generally use look-up tables containing pre-calculated switchingtimes. At run time, look-up tables are routinely selected to providedesired output voltage with optimized THD.

[0013] Because the related art schemes of multilevel inverter controltypically use look-up tables at run time, such related art schemes areunresponsive to real time changes involving multilevel inverters. Inaddition, due to the fact that the control equations are non-linear andnumerous, real time application of such equations is not generallypracticable. Accordingly, a need exists in the art for a method andsystem that can provide multilevel inverter control in a fashion that isless computationally intensive than the control used in related artsystems. In addition, a need exists in the art for a method and systemthat can provide multilevel inverter control in a fashion that isresponsive to real time changes involving multilevel inverters.

BRIEF SUMMARY OF THE INVENTION

[0014] It is a feature and advantage of the present invention to providea method and system of near real time control of multilevel inverters.

[0015] In one embodiment of the present control schemes, a method forcontrolling a multilevel inverter includes but is not limited todetermining at least a peak amplitude of a target waveform; determininga number of discrete steps to achieve the peak amplitude of the targetwaveform; calculating a plurality of switching angles to substantiallyminimize an area difference between the target waveform and a stepsignal of the multilevel inverter, in response to the number of discretesteps; and activating a plurality of voltage sources in response to theplurality of switching angles. In addition to the foregoing, othermethod embodiments are described in the claims, drawings, and textforming a part of the present application. In certain implementationsinvolving a wide DC input voltage range, the disclosed methods may proveparticularly useful.

[0016] In one or more various embodiments, related motorized vehiclesand/or other systems include but are not limited to circuitry and/orprogramming for effecting the herein-referenced method embodiment(s);the circuitry and/or programming can be virtually any combination ofhardware, software, and/or firmware configured to effect theforegoing-referenced method embodiments depending upon the designchoices of the system designer.

[0017] In another embodiment of the present control schemes, amultilevel inverter control system includes but is not limited to meansfor determining at least a peak amplitude of a target waveform; meansfor determining a number of discrete steps to achieve the peak amplitudeof the target waveform; means, responsive to the number of discretesteps, for calculating a plurality of switching angles to substantiallyminimize an area difference between the target waveform and a stepsignal of the multilevel inverter; and means for activating a pluralityof voltage sources in response to the plurality of switching angles. Inaddition to the foregoing, other system embodiments are described in theclaims, drawings, and text forming a part of the present application. Incertain implementations involving a wide DC input voltage range, thedisclosed systems may prove particularly useful.

[0018] In another embodiment of the present control schemes, apower-related device includes but is not limited to means fordetermining at least a peak amplitude of a target waveform; means fordetermining a number of discrete steps to achieve the peak amplitude ofthe target waveform; means for calculating a plurality of switchingangles based on at least one of a frequency and the number of discretesteps to achieve the peak amplitude of the target waveform; and meansfor activating a plurality of voltage sources in response to theplurality of switching angles. In addition to the foregoing, othersystem embodiments are described in the claims, drawings, and textforming a part of the present application. In certain implementationsinvolving a wide DC input voltage range, the disclosed systems may proveparticularly useful.

[0019] In another embodiment of the present control schemes, amultilevel inverter control system includes but is not limited to a stepnumber determination module; and a switch angle determination modulehaving logic configured to substantially minimize an area differencebetween a target waveform and a step signal of a multilevel inverter. Inaddition to the foregoing, other system embodiments are described in theclaims, drawings, and text forming a part of the present application. Incertain implementations involving a wide DC input voltage range, thedisclosed systems may prove particularly useful.

[0020] In another embodiment of the present control schemes, amultilevel inverter control system includes but is not limited to aswitch angle calculation module having logic configured to substantiallyminimize an area difference between a target waveform and a step signalof a multilevel inverter. In addition to the foregoing, other systemembodiments are described in the claims, drawings, and text forming apart of the present application. In certain implementations involving awide DC input voltage range, the disclosed systems may proveparticularly useful.

[0021] The foregoing is a summary and thus contains, by necessity,simplifications, generalizations and omissions of detail; consequently,those skilled in the art will appreciate that the summary isillustrative only and is NOT intended to be in any way limiting. Otheraspects, inventive features, and advantages of the devices and/orprocesses described herein, as defined solely by the claims, will becomeapparent in the non-limiting detailed description set forth herein.

BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)

[0022]FIG. 1 is a system block diagram of multilevel inverter.

[0023]FIG. 2 is a graph of a typical output of multilevel inverters fora quarter cycle.

[0024]FIG. 3 is a graphical representation of a sub-optimal switchingalgorithm.

[0025]FIG. 4 is a graph of a multilevel inverter output with sub-optimalswitching angles.

[0026]FIG. 5 is a block diagram of a control system according to oneillustrated embodiment.

[0027]FIG. 6 is a block diagram of a power-related device that includesa multilevel inverter controller according to one embodiment of thepresent control schemes.

DETAILED DESCRIPTION OF THE INVENTION

[0028] In the following description, certain specific details are setforth in order to provide a thorough understanding of the variousembodiments of the subject matter described herein. However, one skilledin the art will understand that the subject matter described herein maybe practiced without these details. In other instances, well-knownstructures associated with electrical power devices and/or powertransfer devices have not been shown or described in detail to avoidunnecessarily obscuring descriptions of the embodiments of the subjectmatter described herein.

[0029] Unless the context requires otherwise, throughout thespecification and claims which follow, the word “comprise” andvariations thereof, such as, “comprises” and “comprising” are to beconstrued in an open, inclusive sense, that is as “including, but notlimited to.”

[0030] The headings provided herein are for convenience only and do notinterpret the scope or meaning of the claimed invention.

[0031] I. Sub-Optimal Switching Algorithm

[0032]FIG. 2 shows a typical output of a quarter cycle waveform of themultilevel inverter 100. For a quarter wave symmetrical odd functionshown in FIG. 2, there exist only odd numbers of harmonics, including afundamental component. A generalized equation is given, $\begin{matrix}{b_{n} = {{\frac{4}{n\quad \pi}{\sum\limits_{i = 1}^{m}{V_{i}\cos \quad n\quad \alpha_{i}\quad n}}} = {odd}}} & (1)\end{matrix}$

[0033] where b_(n) is the nth harmonic, m is the number of voltage stepsper quarter cycle, and V_(i) is the amplitude of each step voltageincrement. See F. Huang, “NEAR OPTIMAL APPROACH IN THE DESIGN ANDIMPLEMENTATION OF MULTILEVEL VOLTAGE SOURCE INVERTERS”, IEE Proceedings,Electr. Power Appl. Vol. 146, No. 6, November 1999, pp. 661-6, herebyincorporated by reference in its entirety.

[0034] If all the steps have the same amplitude, V_(m), then$\begin{matrix}{b_{n} = {{\frac{4V_{m}}{n\quad \pi}{\sum\limits_{i = 1}^{m}{\cos \quad n\quad \alpha_{i}\quad n}}} = {{odd}.}}} & (2)\end{matrix}$

[0035] The fundamental component (n=1) of the output is $\begin{matrix}{b_{1} = {\frac{4V_{m}}{\quad \pi}{\sum\limits_{i = 1}^{m}{\cos \quad {\alpha_{i}.}}}}} & (3)\end{matrix}$

[0036] It is clear from equation (2) that for 13 steps, 13 non-linearequations need to be solved in order to find the optimal switchingangles α_(i) at a required fundamental output voltage, V₁, and itsharmonics V_(i) (i=3,5, , , ).

[0037] Instead of calculating equation (2), a sub-optimal switchingalgorithm can be used. See F Huang, “NEAR OPTIMAL APPROACH IN THE DESIGNAND IMPLEMENTATION OF MULTILEVEL VOLTAGE SOURCE INVERTERS”, IEEProceedings, Electr. Power Appl. Vol. 146, No.6, November 1999,pp.661-6. This sub-optimal switching algorithm is based on the idea ofminimizing the area between a desired, or target, sinusoidal multilevelinverter output waveform, and the voltage steps used to approximate thetarget waveform.

[0038]FIG. 3 illustrates the idea of the sub-optimal switchingalgorithm. The multilevel inverter 100 switches voltage levels at timesα_(j), α_(i), and α_(k) in an effort to approximate the desired, ortarget, waveform V_(p)sin(α). In the sub-optimal switching algorithm,the goal is to minimize the area difference between the commanded, ortarget, sinusoidal signal V_(p)sin(α) and the step signal from themultilevel inverter 100. With this algorithm, sub-optimal switchingtimes can be found in a very simplified way.

[0039] The area between the two waveforms centered at a step change isshown in FIG. 3 as shaded. Mathematically, this area is expressed as$\begin{matrix}{{F\left( \alpha_{i} \right)} = {{\int_{\alpha_{j}}^{\alpha_{i}}{\left\lbrack {{V_{p}{\sin (\alpha)}} - V_{i - 1}} \right\rbrack {\alpha}}} + {\int_{\alpha_{i}}^{\alpha_{k}}{\left\lbrack {V_{i} - {V_{p}{\sin (\alpha)}}} \right\rbrack {\alpha}}}}} & (4)\end{matrix}$

[0040] where V_(p) is the peak value of the desired (target or command)sine wave, and V_(i) is the step height value of the i^(th) step. At itsminimum, the derivative of the above equation is zero: $\begin{matrix}{{{\frac{\left( {F\left( \alpha_{i} \right)} \right)}{\alpha_{i}} = {{\left\lbrack {{V_{p}{\sin \left( \alpha_{i} \right)}} - V_{i - 1}} \right\rbrack - \left\lbrack {V_{i} - {V_{p}{\sin \left( \alpha_{i} \right)}}} \right\rbrack} = 0}};{or}}\text{}{\alpha_{i} = {\sin^{- 1}\left( \frac{V_{i - 1} + V_{i}}{2V_{p}} \right)}}} & (5)\end{matrix}$

[0041] If the amplitudes of each voltage step are the same, i.e.,V_(i)−V_(i-1)=V_(m), equation (5) can be simplified to, $\begin{matrix}{\alpha_{i} = {\sin^{- 1}\left( {\left( {i - \frac{1}{2}} \right)\frac{V_{m}}{V_{p}}} \right)}} & (6)\end{matrix}$

[0042] where i=1, 2, . . . , m.

[0043] Based on the switching angle calculation in (6), FIG. 4 shows ahalf cycle waveform with five step voltages.

[0044] II. Multilevel Inverter Control System Utilizing Sub-OptimalControl Scheme

[0045] The control of the multilevel inverter 100 is implemented throughtwo stages of control. The first control stage finds a correct number ofvoltage steps for a specific range of input DC bus voltages and outputvoltages. The second control stage fine-tunes the switching angles tocompensate, within a fixed number of voltage steps, variations of theinput DC bus voltage and output load. A hysteretic controller may beused for the first control stage and a PI (Proportional Integral)controller may be used for the second control stage. With the two stagesof control, the output AC voltage follows closely to the commanded, ortargeted, input with the variation of the input DC bus voltage.

[0046]FIG. 5 is a block diagram of a control system 500. The inputs ofthe system are the input DC bus voltage V_(in) 502, the peak value ofthe command, or target, voltage V_(p) 504, and the feedback 506 of theoutput voltage V_(out) (see FIG. 6). The command is the desiredsinusoidal output with its peak value V_(p). The outputs of thecontroller are the switching angles 508 that are fed to a hardwareswitching circuit.

[0047] A. First Control Stage

[0048] The first control stage provides two basic operations (1)determination of the number of steps to be used by the multilevelinverter 100 in order to approximate the command, or target, waveform;and (2) calculation of the switching angles. Consequently, the firstcontrol stage comprises a step number determination module and a switchangle determination module. Although the first control stage isdescribed herein as working with the second control stage, it is to beunderstood that in one embodiment the first control stage can be usedseparately and independently from the second control stage.

[0049] 1. Step Number Determination Module

[0050] In one embodiment, the step number determination module comprisesa hysteretic controller module 510. The hysteretic controller module 510accepts step amplitude V_(m). The step amplitude V_(m) is a function ofthe transformer windings and the DC bus voltage (see FIG. 1). Once thetransformer is selected, the step amplitude V_(m) is substantially onlya function of the input DC bus voltage V_(in) 502. The step amplitudeV_(m) changes proportionally to the input DC bus voltage V_(in) 502. Fora specific hardware configuration, a scaler 516 may optionally be usedto relate the input DC bus voltage Vin 502 and the step amplitude V_(m).

[0051] In order to maintain a consistent multilevel inverter 100 outputvoltage waveform when the DC bus voltage V_(in) 502 is changing in realtime, the number of steps of the multilevel inverter is preferablychanged in accordance with real time changes in the input DC bus voltageV_(in) 502. In one embodiment, the selection of the number of steps isimplemented with the hysteretic controller module 510. The hystereticcontroller module 510 compares the command or target voltage (thedesired output voltage), in the form of peak value of the command, ortarget voltage, V_(p), with the peak value of the fundamental frequencycomponent of the fed-back actual output voltage V_(out) 506. Thefundamental frequency component of the actual output voltage feedback isextracted with a digital filter 528. The digital filter's 528 input isthe measured output voltage V_(out) 506 of the multilevel inverter 100(see FIG. 6). In one embodiment, if the difference between the command,or target, voltage and the feedback signal (measured output of themultilevel inverter 100) is larger than one half of the step amplitude,the step number is increased/decreased by the hysteretic controllermodule 510.

[0052] 2. Switch Angle Determination Module

[0053] In one embodiment, the switch angle determination modulecomprises a switch angle calculation module 514 and a switch anglecorrection factor module 515. The switch angle calculation module 514calculates the switching angles based on input parameters. The switchangle correction factor module 515 calculates and applies a near realtime switching angle correction factor based on the error between thepeak value of the command (or target) voltage V_(p) and the calculatedpeak value V₁ of the fundamental component of the output voltage of themultilevel inverter 100.

[0054] a) Switch Angle Calculation Module

[0055] As described above, once the input DC bus voltage V_(in) 502 andthe command (or target) voltage V_(p) 504 are determined, the hystereticcontroller module 510 receives the step amplitude V_(m) and the command(or target) voltage V_(p) 504 and determines the number of steps, m,necessary to achieve the command (or target) voltage V_(p) 504.

[0056] The switch angle calculation module 514 accepts as input thecommand (or target) voltage V_(p) 504, the number of steps, m, and thestep amplitude V_(m). In one embodiment, logic within the switch anglecalculation module 514 calculates the output switching angles, α_(i)′,using equation (6) above:$\alpha_{i}^{\prime} = {{\sin^{- 1}\left( {\left( {i - \frac{1}{2}} \right)\frac{V_{m}}{V_{p}}} \right)}.}$

[0057] As shown in FIG. 5, switching angles are functions of V_(m) andV_(p). With m steps, the number of switching angles is m. Although notshown, in another embodiment the switch angle calculation module 514calculates the output switching angles, α_(i)′, using equation (5)above: α_(i)′=sin⁻¹((V_(i-1)+V_(i))/2V_(p))).

[0058] In one embodiment of the present control schemes, the switchingangles produced by the switch angle calculation module 514 are used todirectly control the multilevel inverter 100. In another embodiment ofthe present control schemes, the switching angles produced by the switchangle calculation module 514 are corrected in near real time in responseto a monitored output signal. The switch angle correction factor module515 calculates and provides the correction of the switching angles.

[0059] b) Switch Angle Correction Factor Module

[0060] The switch angle correction factor module 515 compensates thecalculated switching angles with a correction factor. The purpose ofcompensation is to increase the output voltage resolution and accuracy.

[0061] In one embodiment, the correction factor is generated with aproportional integral (PI) voltage regulator 518 that is described indetail below. Multiplier 520 multiplies the switching angles α_(i)′ bythe correction factor to generate actual switching angles [α₁, α₂, . . ., α_(m)].

[0062] Notice that the switching angles described above are only for thefirst quadrant, [0, π/2], of the cycle. Using the symmetrical propertyof the sinusoidal signal, the switching angles for the second quadrantare determined as [π-α_(m), . . . , π-α₂, π-α₁]. The rest of theswitching angles over the entire cycle follow the same symmetricalproperty.

[0063] The hysteretic controller module 510 regulates the output voltageby changing the number of voltage steps, m, to compensate for largeinput DC bus voltage V_(in) 502 changes. Once the number of voltagesteps is fixed, or if the variation of the input DC bus voltage V_(in)502 is within one half of the step amplitude V_(m), any smaller input DCbus voltage V_(in) 502 changes can be compensated by adjusting theswitching angles through use of the correction factor generated by thePI voltage regulator 518.

[0064] The PI voltage regulator 518 accepts as input an error signalindicating a difference between the peak value of the command, ortarget, voltage VP 504 and a calculated peak value V₁ of the fundamentalcomponent of a waveform produced with the actual switch angles [α₁, α₂,. . . , α_(m)]. The fundamental peak value determination unit 512calculates an expected peak value, V₁, of the fundamental componentbased upon equation (3), described above.

[0065] As described above, for a given number of steps m, and for n=1,using equation (3) the fundamental component of the multilevel inverter100 output is theoretically$b_{1} = {\frac{4V_{m}}{\pi}{\sum\limits_{i = 1}^{m}{\cos \quad {\alpha_{i}.}}}}$

[0066] The fundamental peak value determination unit 512 uses theforegoing equation, and the actual switching times [α₁, α₂, . . . ] fromthe multiplier 520, to calculate the peak value of the fundamental.

[0067] Where α_(i) is a set of switch-on times in the first quarter ofthe period, therefore, 0<α_(i)<π/2. Since the function of cosine is amono-decreasing function in the domain of [0, π/2], decreasing α_(i)will increase the fundamental component, b₁, of the inverter output.

[0068] The fundamental peak value determination unit 512 outputs thecalculated peak value, V₁, of the fundamental component to thecomparison unit 522. The comparison unit 522 generates an error signalbased on a comparison of the calculated peak value V₁ of the fundamentalcomponent of the output voltage with the peak value of the command (ortarget) voltage V_(p). The error signal of comparison unit 522 isaccepted as the input of the PI voltage regulator 518.

[0069] The output δ of the PI voltage regulator 512, which in oneembodiment ranges from −1<δ<1, is accepted by the summing unit 524 andsummed with a unity one. The output of the summing unit 524, the sum(1-δ), is accepted as input to the multiplier 520. The multiplier 520multiplies the calculated switching angles [α₁′, α₂′, . . . , α_(m)′] bythe sum (1-δ) to produce the corrected switching angles [α₁, α₂, . . . ,α_(m)]. That is, the sum (1-δ), is used as a correction factor tocorrect the calculated switching angles [α₁′, α₂′, . . . , α_(m)′]Thecorrected switching angles are [α₁, α₂, . . . , α_(m)]=(1-δ)[α₁′, α₂′, .. . , α_(m)′]. In one embodiment, the corrected switching angles areused to control the multilevel inverter 100.

[0070] The PI voltage regulator 518 increases the accuracy of themultilevel inverter 100 output within a small variation of input DC busvoltage V_(in) 502. Even though the same correction factor (1-δ) isapplied to all the switching angles, the corrected switching angles arevery close to the switching angle changing trend calculated usingmathematical theory in J. Chiasson, etc., “Real-Time Computer Control ofa Multilevel Converter using the Mathematical Theory of Resultants”,Electrimacs, August 2002.

[0071]FIG. 6 shows a block diagram of a power-related device 600 havingthe control system 500 of FIG. 5 interfaced with and controlling themultilevel inverter 100 of FIG. 1. A system designer may interface thecontrol system 500 with the multilevel inverter 100 using conventionaltechniques. A system designer may incorporate the control system 500 andthe multilevel inverter 100 into the power-related device 600 usingconventional techniques. The power-related device 600 may be virtuallyany type of application utilizing a multilevel inverter, such as amotorized vehicle (e.g., including but not limited to an electricvehicle, a hybrid-electric vehicle, and a fuel-cell powered vehicle), astationary power system, an uninterruptible power supply (UPS), etc.

[0072] Those having ordinary skill in the art will recognize that thereare several identifiable advantages associated with the above-describedschemes. One advantage is that the above-described schemes are such thatthe source of the input DC bus voltage V_(in) 502 can be virtually anytype of DC voltage source, such as rectified DC, battery, fuel cell,solar array, etc. This is because the above-described schemes are suchthat they allow the input DC bus voltage V_(in) 502 to vary in a widerange. The above-described schemes also provide additional advantages,including, but not limited to suitability for a wide range of input DCvoltage, provision of low THD content and high resolution of the outputvoltage, as well as ease of implementation.

[0073] All of the above U.S. patents, U.S. patent applicationpublications, U.S. patent applications, foreign patents, foreign patentapplications and non-patent publications referred to in thisspecification and/or listed in the Application Data Sheet, areincorporated herein by reference, in their entirety. From the foregoingit will be appreciated that, although specific embodiments of theinvention have been described herein for purposes of illustration,various modifications may be made without deviating from the spirit andscope of the invention. Accordingly, the invention is not limited exceptas by the appended claims.

1. A method of controlling a multilevel inverter comprising: determiningat least a peak amplitude of a target waveform; determining a number ofdiscrete steps to achieve the peak amplitude of the target waveform;calculating a plurality of switching angles to substantially minimize anarea difference between the target waveform and a step signal of themultilevel inverter, in response to the number of discrete steps; andactivating a plurality of voltage sources in response to the pluralityof switching angles.
 2. The method of claim 1 wherein the determining atleast a peak amplitude of a target waveform comprises: accepting thepeak amplitude with a hysteretic controller.
 3. The method of claim 1wherein the determining a number of discrete steps to achieve the peakamplitude of the target waveform comprises: filtering an output of themultilevel inverter to extract a fundamental frequency componentwaveform from the output of the multilevel inverter; determining a peakamplitude of the fundamental frequency component waveform; comparing thepeak amplitude of the fundamental frequency component waveform againstthe peak amplitude of the target waveform; and adjusting the number ofdiscrete steps in response to the comparison.
 4. The method of claim 1wherein the calculating a plurality of switching angles to substantiallyminimize an area difference between the target waveform and a stepsignal of the multilevel inverter, in response to the number of discretesteps comprises: calculating each of the plurality of switching anglesas$\alpha_{i}^{\prime} = {\sin^{- 1}\left( {\left( {i - \frac{1}{2}} \right)\frac{V_{m}}{V_{p}}} \right)}$

where V_(m) is a discrete voltage step magnitude, V_(p) is the peakamplitude of the target waveform, and i is an indice ranging from 1 tom, where m is the number of discrete steps.
 5. The method of claim 1wherein the calculating a plurality of switching angles to substantiallyminimize an area difference between the target waveform and a stepsignal of the multilevel inverter, in response to the number of discretesteps comprises: calculating each of the plurality of switching anglesas α_(i)′=sin⁻¹((V_(i-1)+V_(i))/2V_(p)) where V_(i) are V_(i-1) arediscrete voltage step magnitudes indexed against i, V_(p) is the peakamplitude of the target waveform, and i is an indice ranging from 1 tom, where m is the number of discrete steps.
 6. The method of claim 1wherein the activating a plurality of voltage sources in response to theplurality of switching angles comprises: energizing a plurality oftransformers.
 7. The method of claim 1 wherein the calculating aplurality of switching angles to substantially minimize an areadifference between the target waveform and a step signal of themultilevel inverter, in response to the number of discrete stepscomprises: calculating a peak amplitude of a fundamental frequencycomponent waveform; comparing the calculated peak amplitude of thefundamental frequency component waveform against the peak amplitude ofthe target waveform to obtain an error signal; generating a correctionfactor in response to the error signal; and multiplying at least one ofthe plurality of switching angles by the correction factor.
 8. Themethod of claim 7 wherein the generating a correction factor in responseto the error signal comprises: accepting the error signal into an inputof a proportional integral controller; and summing an output of theproportional integral controller with a constant.
 9. A multilevelinverter control system, the control system comprising: means fordetermining at least a peak amplitude of a target waveform; means fordetermining a number of discrete steps to achieve the peak amplitude ofthe target waveform; means, responsive to the number of discrete steps,for calculating a plurality of switching angles to substantiallyminimize an area difference between the target waveform and a stepsignal of a multilevel inverter; and means for activating a plurality ofvoltage sources in response to the plurality of switching angles. 10.The control system of claim 9 wherein the means for determining at leasta peak amplitude of a target waveform comprises: means for accepting thepeak amplitude.
 11. The control system of claim 9 wherein the means fordetermining a number of discrete steps to achieve the peak amplitude ofthe target waveform comprises: means for filtering an output of themultilevel inverter to extract a fundamental frequency componentwaveform from the output of the multilevel inverter; means fordetermining a peak amplitude of the fundamental frequency componentwaveform; means for comparing the peak amplitude of the fundamentalfrequency component waveform against the peak amplitude of the targetwaveform; and means for adjusting the number of discrete steps inresponse to the comparison.
 12. The control system of claim 9 whereinthe means, responsive to the number of discrete steps, for calculating aplurality of switching angles to substantially minimize an areadifference between the target waveform and a step signal of themultilevel inverter comprises: means for calculating each of theplurality of switching angles as$\alpha_{i}^{\prime} = {\sin^{- 1}\left( {\left( {i - \frac{1}{2}} \right)\frac{V_{m}}{V_{p}}} \right)}$

where V_(m) is a discrete voltage step magnitude, V_(p) is the peakamplitude of the target waveform, and i is an indice ranging from 1 tom, where m is the number of discrete steps.
 13. The control system ofclaim 9 wherein the means, responsive to the number of discrete steps,for calculating a plurality of switching angles to substantiallyminimize an area difference between the target waveform and a stepsignal of the multilevel inverter comprises: means for calculating eachof the plurality of switching angles as α_(i)′=sin⁻¹ ((V _(i-1) +V_(i))/2V _(p)) where V_(i) are V_(i-1) are discrete voltage stepmagnitudes indexed against i, V_(p) is the peak amplitude of the targetwaveform, and i is an indice ranging from 1 to m, where m is the numberof discrete steps.
 14. The control system of claim 9 wherein the meansfor activating a plurality of voltage sources in response to theplurality of switching angles comprises: means for energizing aplurality of transformers.
 15. The control system of claim 9 wherein themeans, responsive to the number of discrete steps, for calculating aplurality of switching angles to substantially minimize an areadifference between the target waveform and a step signal of themultilevel inverter comprises: means for calculating a peak amplitude ofa fundamental frequency component waveform; means for comparing thecalculated peak amplitude of the fundamental frequency componentwaveform against the peak amplitude of the target waveform to obtain anerror signal; means for generating a correction factor in response tothe error signal; and means for multiplying at least one of theplurality of switching angles by the correction factor.
 16. The controlsystem of claim 15 wherein the means for generating a correction factorin response to the error signal comprises: means for accepting the errorsignal; and means for summing an output of a proportional integralcontroller with a constant.
 17. The control system of claim 9, furthercomprising: a power-related device including the control system.
 18. Apower-related device comprising: means for determining at least a peakamplitude of a target waveform; means for determining a number ofdiscrete steps to achieve the peak amplitude of the target waveform;means for calculating a plurality of switching angles based on at leastone of a frequency and the number of discrete steps to achieve the peakamplitude of the target waveform; and means for activating a pluralityof voltage sources in response to the plurality of switching angles. 19.A multilevel inverter control system, the control system comprising: astep number determination module; and a switch angle determinationmodule comprising logic configured to substantially minimize an areadifference between a target waveform and a step signal of a multilevelinverter.
 20. The control system of claim 19 wherein the step numberdetermination module comprises a hysteretic controller.
 21. The controlsystem of claim 19 wherein the switch angle determination modulecomprises: a switch angle calculation module; and a switch anglecorrection factor module.
 22. The control system of claim 19 wherein theswitch angle determination module comprises: a switch angle calculationmodule comprising logic configured to calculate each of a plurality ofswitching angles as$\alpha_{i}^{\prime} = {\sin^{- 1}\left( {\left( {i - \frac{1}{2}} \right)\frac{V_{m}}{V_{p}}} \right)}$

where V_(m) is a discrete voltage step magnitude, V_(p) is a peakamplitude of the target waveform, and i is an indice ranging from 1 tom, where m is a number of discrete steps.
 23. The control system ofclaim 19 wherein the switch angle determination module comprises: aswitch angle calculation module comprising logic configured to calculateeach of a plurality of switching angles as α_(i)′=sin⁻¹ ((V _(i-1) +V_(i))/2V _(p)) where V_(i) are V_(i-1) are discrete voltage stepmagnitudes indexed against i, V_(p) is a peak amplitude of the targetwaveform, and i is an indice ranging from 1 to m, where m is a number ofdiscrete steps.
 24. The control system of claim 19 wherein the switchangle determination module comprises: a proportional integral voltageregulator.
 25. The control system of claim 19 wherein the switch angledetermination module comprises: a fundamental peak value determinationunit comprising logic configured to calculate a peak amplitude of thefundamental frequency component waveform as$b_{1} = {\frac{4V_{m}}{\pi}{\sum\limits_{i = 1}^{m}{\cos \quad \alpha_{i}}}}$

where V_(m) is a discrete voltage step magnitude, and i is an indiceranging from 1 to m, where m is a number of discrete steps.
 26. Thecontrol system of claim 19, further comprising: a power-related devicewherein the control system is integrated with the power-related device.27. A multilevel inverter control system, the control system comprising:a switch angle determination module comprising logic configured tosubstantially minimize an area difference between a target waveform anda step signal of a multilevel inverter.
 28. The control system of claim27 wherein the switch angle determination module comprises: a switchangle calculation module comprising logic configured to calculate eachof a plurality of switching angles as$\alpha_{i}^{\prime} = {\sin^{- 1}\left( {\left( {i - \frac{1}{2}} \right)\frac{V_{m}}{V_{p}}} \right)}$

where V_(m) is a discrete voltage step magnitude, V_(p) is a peakamplitude of the target waveform, and i is an indice ranging from 1 tom, where m is a number of discrete steps.
 29. The control system ofclaim 27 wherein the switch angle determination module comprises: aswitch angle calculation module comprising logic configured to calculateeach of a plurality of switching angles as α_(i)′=sin⁻¹ ((V _(i-1) +V_(i))/2V _(p)) where V_(i) are V_(i-1) are discrete voltage stepmagnitudes indexed against i, V_(p) is a peak amplitude of the targetwaveform, and i is an indice ranging from 1 to m, where m is a number ofdiscrete steps.
 30. The control system of claim 27, further comprising:a power-related device wherein the control system is integrated with thepower-related device.